Matrix, MatrixSpace: Add coercion to polymake interface

src/sage/matrix/matrix1.pyx

@@ -344,6 +344,25 @@ cdef class Matrix(matrix0.Matrix):
         s = str(self.rows()).replace('(','[').replace(')',']')
         return "Matrix(%s,%s,%s)"%(self.nrows(), self.ncols(), s)
 
+    def _polymake_(self, polymake=None):
+        """
+        Tries to coerce this matrix to a polymake matrix.
+
+        EXAMPLES::
+
+            sage: M = matrix(ZZ,2,range(4))
+            sage: polymake(M)                   # optional - polymake
+            0 1
+            2 3
+            sage: K.<sqrt5> = QuadraticField(5)
+            sage: M = matrix(K, [[1, 2], [sqrt5, 3]])
+            sage: polymake(M)                   # optional - polymake
+            1 2
+            0+1r5 3
+        """
+        P = polymake(self.parent())
+        return polymake.new_object(P, [ list(r) for r in self.rows(copy=False) ])
+
     def _singular_(self, singular=None):
         """
         Tries to coerce this matrix to a singular matrix.

src/sage/matrix/matrix_space.py

@@ -1773,6 +1773,21 @@ def _magma_init_(self, magma):
             s = 'RMatrixSpace(%s,%s,%s)'%(K.name(), self.__nrows, self.__ncols)
         return s
 
+    def _polymake_init_(self):
+        r"""
+        Return the polymake representation of the matrix space.
+
+        EXAMPLES::
+
+            sage: polymake(MatrixSpace(QQ,3))                   # optional - polymake
+            Matrix<Rational>
+            sage: polymake(MatrixSpace(QuadraticField(5),3))    # optional - polymake
+            Matrix<QuadraticExtension>
+        """
+        from sage.interfaces.polymake import polymake
+        K = polymake(self.base_ring())
+        return '"Matrix<{}>"'.format(K)
+
 def dict_to_list(entries, nrows, ncols):
     """
     Given a dictionary of coordinate tuples, return the list given by